Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation

Melanie F. Pradier, Javier González
Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:1086-1115, 2025.

Abstract

Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the geometry of the data manifold, which is crucial to define a meaningful distance for matching, and struggle when covariates are noisy and high-dimensional. In this work, we propose GeoMatching, a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms among the confounding variables. First, we learn a low-dimensional, latent Riemannian manifold that accounts for uncertainty and geometry of the original input data. Second, we estimate treatment effects via matching in the latent space based on the learned latent Riemannian metric. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators, even as we increase input dimensionality, in the presence of outliers, or in semi-supervised scenarios.

Cite this Paper

BibTeX
@InProceedings{pmlr-v275-pradier25a, title = {Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation}, author = {Pradier, Melanie F. and Gonz\'{a}lez, Javier}, booktitle = {Proceedings of the Fourth Conference on Causal Learning and Reasoning}, pages = {1086--1115}, year = {2025}, editor = {Huang, Biwei and Drton, Mathias}, volume = {275}, series = {Proceedings of Machine Learning Research}, month = {07--09 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v275/main/assets/pradier25a/pradier25a.pdf}, url = {https://proceedings.mlr.press/v275/pradier25a.html}, abstract = {Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the geometry of the data manifold, which is crucial to define a meaningful distance for matching, and struggle when covariates are noisy and high-dimensional. In this work, we propose GeoMatching, a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms among the confounding variables. First, we learn a low-dimensional, latent Riemannian manifold that accounts for uncertainty and geometry of the original input data. Second, we estimate treatment effects via matching in the latent space based on the learned latent Riemannian metric. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators, even as we increase input dimensionality, in the presence of outliers, or in semi-supervised scenarios.} }
Endnote
%0 Conference Paper %T Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation %A Melanie F. Pradier %A Javier González %B Proceedings of the Fourth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2025 %E Biwei Huang %E Mathias Drton %F pmlr-v275-pradier25a %I PMLR %P 1086--1115 %U https://proceedings.mlr.press/v275/pradier25a.html %V 275 %X Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the geometry of the data manifold, which is crucial to define a meaningful distance for matching, and struggle when covariates are noisy and high-dimensional. In this work, we propose GeoMatching, a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms among the confounding variables. First, we learn a low-dimensional, latent Riemannian manifold that accounts for uncertainty and geometry of the original input data. Second, we estimate treatment effects via matching in the latent space based on the learned latent Riemannian metric. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators, even as we increase input dimensionality, in the presence of outliers, or in semi-supervised scenarios.
APA
Pradier, M.F. & González, J.. (2025). Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation. Proceedings of the Fourth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 275:1086-1115 Available from https://proceedings.mlr.press/v275/pradier25a.html.

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